Problem: Solve for $x$ and $y$ using substitution. ${5x+y = 7}$ ${y = -6x+9}$
Explanation: Since $y$ has already been solved for, substitute $-6x+9$ for $y$ in the first equation. ${5x + }{(-6x+9)}{= 7}$ Simplify and solve for $x$ $5x-6x + 9 = 7$ $-x+9 = 7$ $-x+9{-9} = 7{-9}$ $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {y = -6x+9}\thinspace$ to find $y$ ${y = -6}{(2)}{ + 9}$ $y = -12 + 9$ $y = -3$ You can also plug ${x = 2}$ into $\thinspace {5x+y = 7}\thinspace$ and get the same answer for $y$ : ${5}{(2)}{ + y = 7}$ ${y = -3}$